Continuously varying dielectric constant electromagnetic lens



Aug. 28, 1956 M, w. P. sTRANDBl-:RG ETAL 2,761,141

CONTINUOUSLY VARYING DIELECTRIC CONSTANT ELECTROMAGNETIC LENS Filed Aug. 28, 1951 Elf- .arme fr* Y .vl l I CONTINUOUSLY VARYING DIELECTRIC CON- STANT ELECTROMAGNETIC LENS Malcolm ,W. P. Strandberg, Marshfield Hills, and Russell W. Col-kum', Everett, Mass., assignors to the United v'States of America as represented by the Secretary of theAirForce Appucaun August 25s, 1951, serial No. 244,086

l s claims. (ci. 343-911) y (Granted under Title' 3s, U. s. code (1952)', sec. 266) It is old in the art to make a lens of that type byvselecting various pieces of material having different dielectric vconstant and laminating those pieces'in such a manner that the dielectric constant of the laminated body varies in cross section. That type of electromagnetic lens is difficult to construct and further has a disadvantagev that the dielectric constant of the lens varies in steps rather than uniformly as is desired.

It is an object of this invention to provide a dielectric material in which the dielectric constant varies uniformly in the cross section of the dielectric material.

It is another object of this invention to provide a simple, accurate and effective method of constructing a dielectric material having the dielectric constant which varies uniformly in its cross section.

These and other objects and advantages of this invention will become more clear and will best be understood by the following description taken in conjunction with the drawings wherein:

Figure la is a perspective view of a piece of dielectric material having a uniform dielectric constant and shaped in a predetermined manner. l

Figure lb is a perspective view of the piece of dielectric material showing in Figure 1a after it has been deformed by applying pressure.

Figure 2a is a perspective view of a piece of dielectric material similar to the piece illustrated in Figure la except that it is shaped in a different manner.

Figure 2b is a perspective view of the piece of dielectric material of Figure 2a after it has been deformed by applying pressure.

Figure 3 is a perspective view of the plurality of pieces ofdielectric material such as the pieces shown in Figure 2b in which the pieces are stacked to simulate a sphere.

Figure 4 is a graph illustrating the dielectric constant of materials having a fractional volume of polystyrene.

Figure 5 is a graph showing dielectric constant relative density of polystyrene.

The material most suitable for use in making the dielectric material of this invention is Styrofoam which is a foam of a thermo plastic dielectric synthetic resin suchas polystyrene. Other materials which may be used are polymethylmethacrylate and copolymers of vinyl chloride and vinyl acetate, or of methylmethacrylate and styrene. It will be understood however that these are merely examples and that any material may be used which has the characteristic of having a uniform low loss United States Patent dielectric constant and which may formed by pressure.

The dielectric constant of a material which is a mixture of two dielectricmatenals is:

Where e, and e, are the dielectric constanst of the constituent materials and` em is the dielectric constant of the mixture. Also, ka and b are the fractional volumes be shaped and then deem: ela. 62h

em=2.55a A plot of em vs. a is shown in Figure'4.

Referring now to Figure 11a, in order to make apiece of dielectric material in which the 'dielectric constant varies along the length of the material, a block of polystyrene 'foam is shaped by cutting to a shape such as illustrated in Figure la. The material is then placed in a press and the slab of uniform cross section is produced such as that as shown in Figure lb.v Since the density of the material in the slab of Figure lbvvaries along its length, the dielectric will also vary along its length.l The relationship between the dielectric constant and the density will be such as that shown in the graph of Figure 5.

It will be seen from the graph of Figure 5 that the dielectric constant does not have a linear relationship to the relative density, it will therefore be necessary that this non-linear relationship be taken into account when the material is rst cut.

In order to make a circular disk in which the dielectric constant varies radially from the center of the disk, a piece of Styrofoam is rst cut or suitably shaped to the shape shown in Figure 2a. Pressure is then applied until the material has a ilat, disk shape. Theresulting piece of dielectric material shown in Figure 2b may be referred to as an electromagnetic lens of the two dimensional type.4

To make an electromagnetic lens of the three dimensional type., a plurality of disks of the type shown inFigure 2b having different diameters are made. The disk having the larger diameter has a dielectric constant at its center which is greater than the dielectric constant at the center of the disk which adjoins it and the next disk has a smaller dielectric constant and so on. The stack of disks thus formed is shown, as noted in the identification of Figure 3 above, as simulating a sphere. As may be seen from Figure 3 the central disc of the stack has a diameter equal to the great circle diameter of the sphere and the other discs have diameters equal to minor circle diameters of the sphere. From Figure 3 it may -be seen tha-t each of the discs of the stack which simulates the sphere is of the same thickness at the outer periphery of the disc and in view of the fact noted above that each disc is of the type shown in Figure 2b which has been fabricated from pieces of dielectric material of the shape shown in Figure 2a but differing only in diameter, it necessarily follows that each disc will have the same density and hence the same dielectric constant at its outer periphery since the density at this point is obviously substantially that of the uncompressed material. The stack of discs may be machined to give the shape of a sphere and fastened together by means of a proper adhesive or by inclosing the sphere in a spherical sheet of thin dielectric material.

While we have, in accordance with the statutes, illustrated and described a particular embodiment of our invention, it will be understood that many modifications, omissions and additions may be made without departing from the spirit and scope of our invention.

What is claimed is:

1. The method of making a variable dielectric constant lens for electromagneticjwaves which comprisestshaping a piece of dielectric material havingy a: uniform :density t 2 t andhence a uniform dielectric constant to a shape such' f .that its cross `section varies in; height in such a manner that the height 'at' any point' along the crossjsectioni is proportional to the desired magnitude of `dielectric constant f f of the llens at that point, `and lthenapplying pressure to cause the materiall to haveanniformheght and hence afvariable dielectric constant 'iny f a variable density and cross section. i

2. A twoy dimensinal electromagnetic lens comprising a disk of a single foamlike dielectric material of suhl' stantially uniform thickness, all Lof the foam forming rnaterial being'ofthesaniefcomposition; the density of the central portion of said disk being greater than the density 1y from the center tov thezperipherywhereby said disk has a continuously varyingkdierlectric constant from the center n ,3; Anfelectromagnetic rlens lcomprising a stack of di-k electric disks, they thickness ofy said stack of disksj beingi i substantiallyeqnal tothe diameter of the Icenter of said l stack,v each of saidy dskslbeing constituted fof: a `single dii" i electric yfoamlike material, the density of the centralpoiff i tion ofeachi ofsaid disks beinggreater than the density of f rthe peripheral portion of rvsaid disks; said disks varying@ 4.AnI electromagnetic lens comprising astackof diof the peripl'reralportion,k the density varying continnons y f continuously in density from-the ycenter tothe'periphery.' f

electric disks,y the thicknessof saidA stack, of disksL `being substantially equal to the diameter ofthecenterofsaid 30 f l stack, each :of'saiddisks beinglconsttuted ,of a singledivelectric'foainlike material, the density of the cent1-alpen t y tion of each of said disks'beingy greater than thel dens'ityofy i f the peripheral portion of said disks, said disks varying,

' continuously in density vfrom the center; tol the periphery,

said disks decreasing in diameter from'thefcenter to yther kend of tinsstack` whereby said stack is substantially spherical.

5. An electromagnetic lens comprising ra stack ofy `di-y v l electric disks, :the thickness: of said stack of disks being substantially; equal to :the diameterof the center of said stack, each of said disks being constitutedfof a single da v t v :electric foamlike materiaLthe density of the central por- 'disks vdecreasing-in proportionto y.the distance ofl the disk from the center whereby they dielectricconstantalongthe. y n i axial fandtransverse diameters is substantially equal.v

" References; Cited in `the tile'ofthispatent v Y v y y v I y `UNITED STATES PATENTS `Southworth..; i;c..;aSept. y13, 1938 v fernen yniet?rianne,esi a a Article by McCnaig et al.`,` Modern Plastics, page '10641094202;Marcnt945; g n l Chemical- Company, t n

Styrofoam, 'May 2l, 1947,' technicalr data 'by 'Drawv 1 v n 

